A296710 - OEIS

%I #7 Jan 27 2023 19:23:47

%S 11,12,13,14,15,16,17,21,22,23,24,25,26,31,32,33,34,35,41,42,43,44,51,

%T 52,53,61,62,71,92,93,94,95,96,97,98,101,102,103,104,105,106,107,111,

%U 112,113,114,115,116,121,122,123,124,125,131,132,133,134,141,142

%N Numbers whose base-9 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.

%C A rise is an index i such that d(i) < d(i+1); a fall is an index i such that d(i) > d(i+1). The sequences A296709-A296711 partition the natural numbers. See the guide at A296712.

%H Clark Kimberling, <a href="/A296710/b296710.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-9 digits of 142 are 1,6,7; here #(rises) = 2 and #(falls) = 0, so 142 is in the sequence.

%t z = 200; b = 9; d[n_] := Sign[Differences[IntegerDigits[n, b]]];

%t Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296709 *)

%t Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296710 *)

%t Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296711 *)

%Y Cf. A296709, A296711, A296712.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 08 2018